Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

16

DESCRIPTIVE GEOMETRY

In Fig. 19, M-Nrepresents a straight line in a profile plane and
located by a point M in the first quadrant and by a point N in the
third quadrant.
Fig. 20 shows how the projections of Fig. 19 will appear after
H and V take their position of coincidence.
26. Observations. When a straight line is parallel to a plane of
projection, the projection upon this plane of any definite portion
of the line will be equal in length to the portion in question.
/ / / n/
^^ ^..^.....n'_ _m G
/ FIG. 19 FIG. 20
If a straight line is situated in a plane of projection, the line
itself is its own projection upon this plane.
If a straight line is situated in H, its horizontal projection is the
line itself and its vertical projection is in G-L.
If a straight line is situated in V, its vertical projection is the
line itself and its horizontal projection is in G-L.
If a straight line is parallel to H and oblique to V, its vertical
projection will be parallel to G-L and its horizontal projection
will make the same angle with G-L that the line itself makes
with V.
If a straight line is parallel to Vand oblique to H, its horizontal
projection will be parallel to G-L and its vertical projection
will make the same angle with G-L that the line itself makes
with H.
If a straight line is in a profile plane, its projecting planes
coincide and its projections are perpendicular to G-L.